Burton has been reunited with new Owls boss Dave Jones after only signing a short-term contract at the Hawthorns.
Hodgson will rely on Downing and goalkeeping coach, Dean Kiely, as his backroom team for the time being.
Downing said: "We're disappointed Terry has gone because the relationship we had with him was very good.
"He was always to be here on a temporary contract due to the situation with Dave Jones obviously looking to get back into work.
"We've discussed it and we will carry on as we did when Michael Appleton left (to become Portsmouth manager) a few months earlier. We will carry on with myself, Dean and the gaffer."